PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
80012^242220-11039972916Enzo Doria05/2014
80022^242205-11341372911Enzo Doria07/2014
8003(3^152809+3^76405+1)/772908Serge Batalov03/2014
80042^242175+7424372902Yves Minet03/2011
8005(2^242168+3406)/272900Stefano Morozzi01/2020
80062^242150+1765972895Lelio R Paula11/2009
800718902^7179+7179^1890272888Hans Havermann11/2019
800811^69982-234072879Enzo Doria12/2012
8009(23*2^242093+1)/1011772875Lelio R Paula08/2012
8010(67607*2^242043+1)/3326372863Lelio R Paula06/2014
80112^242032+8772859Lelio R Paula03/2012
8012(2^241983+2690)/272844Stefano Morozzi01/2020
80142^241968-11059572840Enzo Doria05/2014
8013(2^241968+598)/272840Stefano Morozzi01/2020
801518850^7313+7313^1885072839Hans Havermann11/2019
8016(2^241921+3290)/272826Stefano Morozzi01/2020
8017(10^72821+71)/972821Robert Price11/2014
80182^241852-6487572805Lelio R Paula05/2013
8019F(348307)/2056289086590809372776Donovan Johnson07/2007
802013952^17559+17559^1395272776Norbert Schneider09/2019
8021(67*10^72772+23)/972773Ray Chandler11/2010
8022(8*10^72759+67)/372760Robert Price01/2017
80232^241670+14572750Lelio R Paula03/2012
80245^104074+5272745Lelio R Paula08/2014
8025(3^152466-5)/72472742Lelio R Paula06/2012
802620^55908-4172738Lelio R Paula01/2015
8027(73*10^72735+53)/972736Robert Price10/2015
802810^72730+22401172731Patrick De Geest05/2013
802910^72730-9972730Robert Price05/2011
80303*10^72723+6772724Robert Price11/2017
8032(11^69833+3^69833)/1472723Robert Price03/2013
8031(10^72723-79)/372723Robert Price10/2017
803318706^7719+7719^1870672721Hans Havermann11/2019
8034(88*10^72711-43)/972712Robert Price11/2015
80353^152379+28072704Lelio R Paula01/2015
8037(25*10^72703-241)/972704Robert Price01/2017
8036(2^241517+3774)/272704Stefano Morozzi01/2020
8038(2^241515+3518)/272703Stefano Morozzi01/2020
8039(47*10^72696+133)/972697Robert Price04/2017
804017^59077-9072692Lelio R Paula01/2015
804165^40096+5872691Lelio R Paula01/2016
8042(29*2^241446-1)/24572682Lelio R Paula01/2014
804411^69783-3840000072672Enzo Doria01/2013
80432^241409-11290372672Enzo Doria06/2014
804518895^7014+7014^1889572670Hans Havermann11/2019
8046(3^152287+1)/472659Paul Bourdelais04/2008
8047(2^241353+3186)/272655Stefano Morozzi01/2020
804817638^13137+13137^1763872643Hans Havermann11/2019
80493^152249-5672642Lelio R Paula01/2015
805010^72631+3772632Robert Price01/2011
805110^72631-881372631Patrick De Geest05/2013
8052(19*2^241254+1)/10172624Lelio R Paula08/2012
8053(9^76103+8^76103)/1772620Robert Price12/2012
80542^241220-11233772615Enzo Doria06/2014
8055(82*10^72612+449)/972613Robert Price02/2017
80562^241169-1579372600Enzo Doria04/2013
80579*10^72595+1172596Robert Kinser01/2017
8058(2^241152+2478)/272594Stefano Morozzi01/2020
8059(2^241143+2438)/272591Stefano Morozzi01/2020
8060(2^241115+1598)/272583Stefano Morozzi01/2020
8061(25*2^241048+1)/8972563Lelio R Paula08/2012
8062(2^241045+1550)/272562Stefano Morozzi01/2020
8063(22*10^72560+17)/372561Robert Price09/2015
80642^241032-2372558Lelio R Paula02/2012
806534485*10^72550+2^241004-372555Gilbert Mozzo12/2012
806619460^5349+5349^1946072553Hans Havermann11/2019
8067(2^241016+3850)/272553Stefano Morozzi01/2020
80682^241004-372550M. Frind & P. Underwood07/2002
806922061^1942+1942^2206172543Hans Havermann11/2019
807097*10^72522-372524Robert Price01/2017
8071(68*10^72516+7)/372518Robert Price03/2016
8072(78557*2^240844+1)/6372505Lelio R Paula06/2014
807367^39701-6672497Norbert Schneider11/2014
8074(185*10^72484+7)/372486Robert Price02/2017
8075(2^240780+2686)/272482Stefano Morozzi01/2020
8076(2^240759+1106)/272476Stefano Morozzi01/2020
8077(293*27^50631-1736)/1372473Curtis Bright05/2015
8078103^36005-10272473Norbert Schneider10/2016
807915^61616+8872467Lelio R Paula01/2015
808045^43831+272462Lelio R Paula05/2013
80812^240692-49238972456Paul Bourdelais03/2013
8082(646*10^72446-7)/972448Robert Price07/2016
80839*6^93083+772434Lelio R Paula10/2014
80842^240617-364572433Lelio R Paula05/2013
808511^69531-2400072410Enzo Doria12/2012
808618714^7367+7367^1871472373Hans Havermann11/2019
8087(22699*2^240396+1)/5572370Lelio R Paula06/2014
80886^92995+1372365Lelio R Paula01/2015
8089(11*10^72362-149)/372363Robert Price01/2017
809018567^7892+7892^1856772360Hans Havermann11/2019
8091(2^240381+3)/5165572358Lelio R Paula05/2012
80926^92974-5572348Lelio R Paula01/2015
80932^240295+1172337Lelio R Paula02/2012
8094(2^240294+1342)/272336Stefano Morozzi01/2020
8095(14*10^72326-53)/372327Robert Price12/2016
809615^61493-4672322Lelio R Paula01/2015
8097(2^240245+2094)/272321Stefano Morozzi01/2020
8098(2^240237+1554)/272319Stefano Morozzi01/2020
8099lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
8100(2^240211+1514)/272311Stefano Morozzi01/2020
81025*10^72302+972303Dmitry Domanov11/2010
8101(9787*2^240179-1)/26572303Lelio R Paula04/2015
8103(2^240171+3246)/272299Stefano Morozzi01/2020
810411^69419-312072293Enzo Doria12/2012
810518069^10016+10016^1806972289Hans Havermann11/2019
8106(2^240095+594)/272276Stefano Morozzi01/2020
81074*10^72274-8372275Robert Price10/2017
8108(2^240075+2790)/272270Stefano Morozzi01/2020
810910^72267+3372268Robert Price01/2011
811010^72267-55394772267Patrick De Geest05/2013
8111(2^240066+1030)/272267Stefano Morozzi01/2020
811311^69389-138072262Enzo Doria12/2012
8114(16^60013-5^60013)/1172262Robert Price07/2013
81127^85507-3072262Lelio R Paula08/2014
8115(19*2^240026-1)/1572256Lelio R Paula02/2014
8116(3^151426-2)/66133772243Lelio R Paula06/2012
8117(2^239940+3850)/272229Stefano Morozzi01/2020
8118gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
81192^239863-11226772206Enzo Doria06/2014
81202^239853-11485372203Enzo Doria05/2015
8121(4*10^72174+149)/972174Robert Price03/2017
8123(2^239671+9)/29613172143Lelio R Paula05/2012
81222^239651-11066572143Enzo Doria05/2014
8124(29*2^239650-1)/330572140Lelio R Paula01/2014
8125241^30280+30280^24172128Norbert Schneider11/2014
8126(2^239603+950)/272128Stefano Morozzi01/2020
8127(2^239594+3058)/272125Stefano Morozzi01/2020
8128(68*10^72120-23)/972121Robert Price10/2015
8129(9^75571+8^75571)/1772112Robert Price12/2012
8130(15*2^239530-1)/17372105Lelio R Paula01/2014
8131(2^239523+2378)/272104Stefano Morozzi01/2020
81322^239513-11251972101Enzo Doria06/2014
8133(10^72097+149)/372097Serge Batalov12/2014
81342^239442-655572080Lelio R Paula05/2012
81352*5^103106+372069Lelio R Paula10/2014
81362^239402-19772068Lelio R Paula02/2012
81372^239356-11187572054Enzo Doria05/2014
8138(38*10^72050-119)/972051Robert Price11/2016
81392^239339+1501572049Lelio R Paula01/2013
8140159^32728+272048Lelio R Paula05/2013
814115^61259-3872047Lelio R Paula01/2015
814292^36683-91^3668372038Robert Price08/2015
81432^239280+5461572031Lelio R Paula05/2012
8144(47*2^239267+1)/7772027Lelio R Paula04/2015
8146(85*10^72025-1)/372027Robert Price07/2017
8145(2^239269+1730)/272027Stefano Morozzi01/2020
81472^239236-9730572018Lelio R Paula05/2012
8149144^33361-14372006Norbert Schneider11/2018
8148(2^239198+1422)/272006Stefano Morozzi01/2020
81502^239169+5971998Lelio R Paula02/2012
8151lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
8152(15*2^239171-1)/10630171994Lelio R Paula01/2014
8153(2^239121+1926)/271983Stefano Morozzi01/2020
8155(29^49211-1)/2871965Robert Price04/2012
8154(299*10^71963+1)/371965Robert Price11/2017
8156L(344293)71953Renaud Lifchitz09/2003
8157V(344293)71953Serge Batalov03/2015
81586*10^71951+771952Dmitry Domanov11/2010
81593^150798+4071949Lelio R Paula01/2015
81602^238961+9571935Lelio R Paula02/2012
816112511^17556+17556^1251171933Norbert Schneider09/2019
81622^238936-40771927Yves Minet02/2012
8163(2^238930+2982)/271925Stefano Morozzi01/2020
81642^238923-2863571923Lelio R Paula05/2012
816510^71910+2511971911Patrick De Geest05/2016
816610^71910-80171910Robert Price04/2016
8167(2^238862+1230)/271905Stefano Morozzi01/2020
8168(2^238864+3198)/271905Stefano Morozzi01/2020
81692^238845-11265171900Enzo Doria06/2014
81702^238792-11124571884Enzo Doria05/2014
81716*7^85059+571884Lelio R Paula10/2014
817219312^5273+5273^1931271881Hans Havermann11/2019
817319176^5603+5603^1917671880Hans Havermann11/2019
81742^238752-11058971872Enzo Doria05/2014
8175(2^238739+2738)/271868Stefano Morozzi01/2020
817612^66581+771853Lelio R Paula07/2014
8177(7*2^238691+1)/4122971850Lelio R Paula06/2012
81784*3^150568-571840Lelio R Paula04/2014
81796^92301+6771825Lelio R Paula01/2015
81802^238568+9876533171817Jason Earls01/2009
81812^238541-11272371808Enzo Doria06/2014
81822^238529-1594971805Enzo Doria04/2013
81839*5^102721-871800Lelio R Paula10/2014
81842^238494-16571794Lelio R Paula02/2012
818518035^9562+9562^1803571790Hans Havermann10/2019
818618390^7993+7993^1839071771Hans Havermann11/2019
81872^238389-11090571763Enzo Doria05/2014
8188(145*10^71760-1)/971762Serge Batalov12/2014
81897^84913+506271760Mike Oakes02/2010
819021218^2409+2409^2121871756Hans Havermann10/2019
8191(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
81922^238268-9730571726Lelio R Paula05/2012
8193gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
8194(2^238249+3770)/271720Stefano Morozzi01/2020
81952^238235-11324771716Enzo Doria07/2014
81962*12^66450-5^6645071712Mike Oakes11/2010
8197(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
81982^238199-11181771706Enzo Doria05/2014
8199lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
82002^238144+9876533171689Jason Earls01/2009
8201(2^238137+2810)/271687Stefano Morozzi01/2020
820218^57102-426571679Enzo Doria03/2013
8203(73*10^71670-1)/971671Robert Price01/2015
82042^238081+1155*23808171670Henri Lifchitz02/2005
82052^238067-11192571666Enzo Doria05/2014
8206(2^238024+3690)/271653Stefano Morozzi01/2020
820719143^5528+5528^1914371644Hans Havermann10/2019
820865401!4+12871638Robert Price09/2019
820936^46030+3571637Norbert Schneider04/2014
8210(74*10^71621+313)/971622Robert Price11/2017
82112^237905-9171617Lelio R Paula02/2012
8212(31*2^237902-1)/12371616Lelio R Paula01/2014
8213(15185*2^237866-1)/4396771605Lelio R Paula04/2015
821416696^16957+16957^1669671603Norbert Schneider09/2019
8215(24737*2^237841+1)/2571601Lelio R Paula06/2014
82162^237846+129971599Lelio R Paula05/2012
82176^92004+19980171594Mike Oakes02/2011
8218159^32516+271581Lelio R Paula05/2013
82192^237781+85571580Lelio R Paula05/2012
8220(2^237754+814)/271571Stefano Morozzi01/2020
82212^237720-407971561Yves Minet06/2011
82222^237698-11094571555Enzo Doria05/2014
82232^237695-11323971554Enzo Doria07/2014
82248*5^102362-971549Lelio R Paula10/2014
8225(4*10^71546-31)/971546Erik Branger05/2011
82262^237650+3771540Lelio R Paula02/2012
822718^56977-439171522Enzo Doria03/2013
8229(22699*2^237565+1)/413663771512Lelio R Paula06/2014
8228((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
8230(26*10^71503+7)/371504Erik Branger11/2013
8231(4*10^71498+173)/371499Robert Price01/2017
82323^149848+11071496Lelio R Paula11/2014
82332^237498+51371495Lelio R Paula05/2012
82342^237485+10771491Lelio R Paula02/2012
8235(2^237465+9)/241971481Lelio R Paula05/2012
82362^237439-11223771477Enzo Doria06/2014
8237(2^237427+2510)/271473Stefano Morozzi01/2020
82382^237407-978771467Lelio R Paula11/2009
82392^237383+7295371460Enzo Doria04/2016
824019768^4119+4119^1976871458Hans Havermann11/2019
824182^37337-81^3733771457Robert Price01/2015
8242(1017*2^237313-1)/1971441Lelio R Paula04/2015
82432^237311+19171438Lelio R Paula02/2012
824411699^17560+17560^1169971437Norbert Schneider09/2019
82452^237280-5971429Lelio R Paula02/2012
8246(2^237275+1038)/271427Stefano Morozzi01/2020
8247(2^237265+2774)/271424Stefano Morozzi01/2020
824811^68564-9871403Lelio R Paula01/2015
82492^237173+7480171397Enzo Doria04/2016
8250(2^237150+1458)/271389Stefano Morozzi01/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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